# 5.79 Traffic Fatalities and Intoxication. The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is 0.40 that a traffic fatality will involve an intoxicated or alcohol-impaired driver or nonoccupant. In eight traffic fatalities, nd the probability that the number, Y , that involve an intoxicated or alcohol-impaired driver or nonoccupant isa. exactly three; at least three; at most three.b. between two and four, inclusive.c. Find and interpret the mean of the random variable Y .d. Obtain the standard deviation of Y .

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5.79 Traffic Fatalities and Intoxication. The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is 0.40 that a traffic fatality will involve an intoxicated or alcohol-impaired driver or nonoccupant. In eight traffic fatalities, nd the probability that the number, Y , that involve an intoxicated or alcohol-impaired driver or nonoccupant is

a. exactly three; at least three; at most three.
b. between two and four, inclusive.
c. Find and interpret the mean of the random variable Y .
d. Obtain the standard deviation of Y .

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Step 1

(a)

The random variable Y is the number of traffic fatality that involves an intoxicated or alcohol-impaired driver or non-occupant and a random sample (n) of 8 traffic fatalities is taken.

The two possible outcomes are the traffic fatality that involves an intoxicated or alcohol-impaired driver or non-occupant or the traffic fatality does not involve an intoxicated or alcohol-impaired driver or non-occupant (success or failure).

The probability of success (p) is 0.40. Thus, Y follows binomial distribution.

The probability of obtaining Y successes in n independent trails of a binomial experiment is,

Step 2

Substitute values n=8 and p=0.4 in the above equation. Then,

Step 3

Exactly three:

The probability that the number, Y, that involve an intoxicated or alcohol-impaire...

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